Intermediate Macroeconomics - Measurement (Continued) and Production

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					 Intermediate Macroeconomics
Measurement (Continued) and Production




               September 1, 2009




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Measuring Inflation


  Inflation: Percent change in the price level.
      What is the price level?

  Two steps to calculate inflation:
      (1) Measure a proxy for the price level called the price index
      (2) Measure the growth rate of the price index

  There are two famous price indexes:
      GDP Deflator
      Consumer Price Index (CPI)




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GDP Deflator


  The GDP deflator is backed out from real GDP and nominal GDP

      Find the Nominal GDP measure (GDP N )
      Find the Real GDP measure (GDP R )


                                               N
                                            GDPt
                                 ¯
                                 Pt =          R
                                            GDPt

                                             ¯     ¯
                                             Pt+1 −Pt
                            Inflation =          ¯
                                                Pt




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GDP Deflator
  What is the inflation rate (measured by the deflator) in this
  example?




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Consumer Price Index


  The CPI gives the average price of a fixed basket of consumer
  goods
  It is calculated by the Bureau of Labor Statistics (BLS)

      The BLS visits and calls stores, collecting prices

      For any good, they calculate a change in price

      The price changes are weighted by purchasing habits
           Consumer Expenditure Survey (CES)




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Measuring Saving and Wealth

  Saving : (Current Income) minus (Current “used up” Goods)
      Is Investment used up?
      Are Consumer Durables used up?

  National Saving (S): National Income minus “Used Up” Goods
                                      ≈GDPt                Ct +Gt

  Private Saving (S pvt ): Disposable Income minus Consumption
                                    ≈(GDPt −Taxest )           Ct


  Government Saving (S gov ): Gov Income minus Gov Spending
                                               ≈Taxest       Gt
  National Saving = Private Saving + Government Saving
      “Saving”


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Uses for Private Saving


      St = GDPt − Ct − Gt

      St = (Ct + It + Gt + NXt ) − Ct − Gt

      St = It + NXt
          where NX ≈ Current Account (CA)


      Stpvt = It + CAt + (−Stgov )
                                Deficit
          Since St =    Stpvt   + Stgov




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Relating Saving and Wealth


  Back to stock and flow

  Saving is the flow into the stock of national wealth(W)

  St + St+1 + St+2 + ... + ST = WT




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Measuring Interest Rates


      Interest: A fee charged by a lender to a borrower .
      Interest Rate: The fee divided by the amount borrowed
                      FEE
           i=   AMOUNT BORROWED



  Real versus Nominal Interest Rates
      Nominal interest rate (i): The interest rate at current prices
      Real interest rate(r): The interest rate at constant prices

  Fisher Equation:
      i = r+ inflation rate



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Interest Rates




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The Production Function

  Inputs ⇒ Production Function ⇒ Output


                               Y = F (INPUTS)


  Economists call inputs “factors of production”
      Labor (N): Time spent working
      Capital (K): Amount of goods used to make other goods


                                  Y = F (K , N)


  What other types of inputs are we missing?

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Desirable Properties of the Production Function



  Economists want a function with the following properties:

      All inputs ⇑ causes Output ⇑

      Inputs work together to make output

      Holding one input fixed, will make another input not work as
      well




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The Cobb-Douglass Production Function



                                Y = K α N 1−α
                                             F (K ,N)




      Doubling (or tripling, or..) both N and K ⇒ Y to double (or
      triple,..)

          F(2N,2K) = 2Y
          F(3N,3K) = 3Y
          For any z ≥ 0, F(zN,zK) = zY
  This is called Constant Returns to Scale



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The Cobb-Douglas Production Function


                                Y = K α N 1−α
                                             F (K ,N)



  αK = α: Capital’s Share of Output
  αN = 1 − α: Labor’s Share of Output


                                Y = K αK N αN


  Economists have measured αK = 0.3 and αN = 0.7

                                Y = K 0.3 N 0.7


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The Cobb-Douglas Production Function



  What about overall productivity?

  Overall productivity (A) makes all inputs work better:


                                 Y = AF(K,N)


  A is usually called total factor productivity (TFP).




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The Cobb-Douglas Production Function
  Y = F(K,N) is a three-dimensional function:




           Output




                                                    Capital

                                 Labor



  Very complicated to understand what’s going on!
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The Cobb-Douglas Production Function




  So we look at altering one input at a time, holding the other fixed

                        ¯
      If labor is fixed: N
                          ¯
      If capital is fixed: K

  “Fixed” means they are treated as “parameters” (i.e. specific
  numbers, not variables)




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The Cobb-Douglas Production Function

  Holding Labor Fixed




           Y




                             N               K




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The Cobb-Douglas Production Function
  Holding Labor Fixed




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The Marginal Product of Capital

  Holding Labor Fixed:

                                           ¯
                               Y = AF (K , N)


  What happens to output when we adjust capital?

  Notation:
      ∆ means change
      ∆K : change in capital
      ∆Y : change in output

  What happens to ∆Y when we change capital (i.e ∆K = 0)?
                                             ∆Y
  Marginal Product of Capital (MPK) =        ∆K


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The Marginal Product of Capital




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The Marginal Product of Labor



  Holding Capital Fixed:

          ¯
  Y = AF (K , N)

  What happens to output when we adjust labor?

  Same as asking:
  What happens to ∆Y when ∆N = 0?
                                              ∆Y
  Marginal Product of Labor (MPN) =           ∆N




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The Marginal Product of Labor
  Holding Capital Fixed




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Changes in Productivity




  TFP (or A) is considered is considered an exogenous “parameter”
  in most models.
      ∆A: Productivity shock
           Often called supply shock




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Supply (Productivity) Shock




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